island sink drain slow/not drain & toliet slow/not flushing

I've got a 86 trailer which I bought and found i got into some plumbing trouble.

the shower/tub, bath sink, and toliet is at one end of the house and then of course the island is at the front end.

so the island never had a roof vent and only the cheater vent, although i just bought it and never ran the water for an extended period to test the drains.

anyway I started seeing the sink drain slower and slower and now it doesnt drain, so i replaced the entire setup under the island in hopes maybe it would fix the issue but still it wont drain and gurgled at first before the drain stopped working.
I tried drano and such etc...no luck, i do remember the sink pipe had nasty gunk in it (filling 1/4 of the pipe up) and stinks terrible.

now the toliet is not going down but yet the sink and shower work fine in the same bathroom...?

at first i thought its got to be the septic backing up ....But how can the washer, bathsink, and shower all work great but not the toliet and island?

At best you have a long flat run with almost no pitch.
At worst you have a buch of saggin going on,
In any case a snaking is needed.
Getting rid of sags will help keep it working longer And prevent the drain from freezing up in the winter.

You are seeing a major problem with the "cheater ventsAAV". When the drains start to get slow, which is your real problem, the AAV will not let the sink drain. If you remove it, the sink will probably work properly, but you will still have the partially plugged drain problem.